1 Distance decay

A well-documented phenomenon in nature is distance decay— the decreasing species similarity between two locations as the distance between them increase. However, studies addressing distance decay in community structure are rare.


2 Goal

We studied how distance affects the modular structure of a multilayer plant-pollinator network in the Canary Islands. In addition, we performed null models that explicitly control different components to disentangle the mechanisms behind distance decay patterns.


3 Plant-pollinator multilayer network

Contained four components:

  1. Seven layers (six islands and the mainland).

  2. Two sets of nodes representing pollinator and plant species.

  3. Intralayer directed weighted links representing pollinator-plant interactions within layers.

  4. Interlayer weighted links connecting any species i to itself between two layers. Closer two layers are, the stronger is the interlayer link. Ecologically, closer distance increases the likelihood that spatial processes such as dispersal occur between two sites


4 Island level



4.1 Species distance decay


We calculated Jaccard similarity of species identity between islands and tested distance decay using a linear regression model.

4.1.1 Species distance decay - Empirical data


We observed species distance decay between islands in the empirical data (\(R^2\) = 0.74, P < 0.001), which indicates that islands tended to share less species with increasing distance.




4.1.2 Species distance decay- Null model shuffling species between layers (\(M_1\))


We compared the observed distance decay to that obtained using three versions of null model where we shuffled species (plants, pollinators and both) between layers. \(M_1\) changes species labels and interlayer structure but not intralayer structure.


Redistributing plant, pollinator and both species among sites did not break species distance decay (\(R^2_{M_1^P}\) = 0.68, P < 0.001; \(R^2_{M_1^A}\) = 0.71, P < 0.001; \(R^2_{M_1^{AP}}\) = 0.35, P = 0.004). The difference was more pronounced when shuffling both plant and pollinator species, which indicates that both species together have a stronger effect in distance decay.




4.2 Modules distance decay


We calculated distance decay in structure in the same way as for species, but using module identities. In addition, we used multiple null models to disentangle the mechanisms behind the pattern found because differences in structure could emerge due to turnover in species composition or interaction rewiring.

4.2.1 Modules distance decay - Empirical data


The spatial network was partitioned to 88 modules. Most (85) modules were found in more than one island, while 3 modules were confined to a single island. Modules varied in size, ranging from 2 to 44 species, with an average of 7±1 species per module.



We observed modules distance decay in the empirical data (\(R^2\) = 0.67, P < 0.001), which indicates that islands tended to share less modules with increasing distance. However, decay in modules was weaker than for species.




4.2.2 Modules distance decay- Null model shuffling species between layers (\(M_1\))


Similarly to distance decay in species, redistributing plant, pollinator and both species among islands did not break structure distance decay (\(R^2_{M_1^P}\) = 0.59, P < 0.001; \(R^2_{M_1^A}\) = 0.097, P < 0.001; \(R^2_{M_1^{AP}}\) = 0.14, P < 0.001).




In particular, redistributing pollinators and both plants and pollinators between islands affected the amount of variation explained by distance (P < 0.001); but not the redistribution of plant species (P = 0.997).




4.2.3 Modules distance decay- Null model shuffling interactions within layers (\(M_2\))


We tested if local structure affects distance decay in structure by shuffling interactions within layers. \(M_2\) changes the intralayer structure but conserves the interlayer structure of the network.

Shuffling local structure broke distance decay pattern in structure (\(R^2_{M_2}\) = 0.12, P = 0.12) and had a significant effect on the overall structure variation explained by distance (P < 0.001).






4.2.4 Modules distance decay- Null model shuffling interactions between layers (\(M_3\))


We tested if rewiring interaction across islands affects distance decay in structure by shuffling interactions of each pair of species between all the islands in which they co-occur. \(M_3\) shuffles intralayer links between islands but conserves the interlayer links.


Shuffling interactions between islands did not break distance decay pattern in structure (\(R^2_{M_3}\) = 0.33, P = 0.006) but had a significant effect on the overall structure variation explained by distance (P < 0.001).






4.2.5 Modules distance decay- Beta diversity components


Shuffling species between islands deviates more from the empirical value than shuffling interactions between islands (t-test, \(R^2_{M_3}\) > \(R^2_{M_2}\), P < 0.001), which indicates species turnover is the main driver of distance decay in structure.




4.2.6 Modules distance decay- Null model uniform value interlayerlinks (\(M_4\))


To test the effect of distance between islands, we fixed the weight of all interlayer links to a uniform value equal to the median of all the interlayer weights in the network. \(M_4\) maintains intralayer structure and the presence of interlayer links.


Contrary to what we expected, fixing the same distance between islands produced a similar pattern of distance decay in modules as the empirical network (\(R^2_{M_4}\) = 0.68, P < 0.001).













5 Site level


5.1 Species distance decay


5.1.1 Species distance decay - Empirical data


We observed species distance decay in the empirical data (\(R^2\) = 0.75, P < 0.001).




5.1.2 Species distance decay- Null model shuffling species between layers (M1)

 
The decay was more pronounced when shuffling plants (\(R^2_{M_1^P}\) = 0.7, P < 0.001) but much less so when shuffling pollinators (\(R^2_{M_1^A}\) = 0.61, P < 0.001) and both species (\(R^2_{M_1^{AP}}\) = 0.17, P < 0.001). These indicate that mainly pollinators has a stronger effect in the distance decay.    






5.2 Modules distance decay


5.2.1 Modules distance decay - Empirical data


We observed modules distance decay in the empirical data (\(R^2\) = 0.56, P < 0.001), which indicates that sites tended to share less modules with increasing distance. However, decay in modules was weaker than for species.







5.2.2 Modules distance decay- Null model shuffling species between layers (M1)


  Similarly to distance decay in species, redistributing plant, pollinator and both species among sites did not break structure distance decay (\(R^2_{M_1^P}\) = 0.075, P = 0.014; \(R^2_{M_1^A}\) = 0.074, P = 0.032; \(R^2_{M_1^{AP}}\) = 0.075, P = 0.014).

 

In particular, redistributing plants did not affect the amount of variation explained by distance (P = 0.952). In contrast, redistributing pollinators (P < 0.001), or both plants and pollinators (P < 0.001) had a significant effect and almost produced distance decay disappear.







5.2.3 Modules distance decay- Null model shuffling interactions within layers (M2)


Shuffling local interaction structure had a significant effect on the overall structure variation explained by distance (P < 0.001) but did not break distance decay pattern in structure (\(R^2_{M_2}\) = 0.05, P = 0.047).









5.2.4 Modules distance decay- Null model shuffling interactions between layers (M3)


Similarly, shuffling interactions between sites did not break distance decay pattern in structure (\(R^2_{M_3}\) = 0.41, P < 0.001) but had a significant effect on the overall structure variation explained by distance (P < 0.001).









5.2.5 Modules distance decay- Beta diversity components


Shuffling species between sites deviates more from the empirical value than shuffling interactions between sites (t-test, \(R^2_{M_3}\) > \(R^2_{M_2}\), P < 0.001), which indicates species turnover is the main driver of distance decay in structure.







5.2.6 Modules distance decay- Null model uniform value interlayerlinks (M4)


In addition, contrary to what we expected, fixing the same distance between locations produces a similar pattern of distance decay in modules as the empirical network (\(R^2_{M_4}\) = 0.51, P < 0.001).